Question

If (3x − 2)(3x + 2) = ax2 − b, what is the value of a?

Answer 1

`\sf{\bold{\blue{\underline{\underline{Given}}}}}`

• (3x − 2)(3x + 2) = ax2 − b⠀⠀⠀⠀

`\sf{\bold{\red{\underline{\underline{To\:Find}}}}}`

• ⠀what is the value of a?⠀⠀⠀

`\sf{\bold{\purple{\underline{\underline{Solution}}}}}`

At first we have to solve the value of (3x-2)(3x+2)

• 
  `\sf{(3x-2)(3x+2) }`

• 
  `\sf{3x(3x+2)-2(3x+2) }`

• 
  `\sf{9x^(2)+6x-6x-4 }`

• 
  `\sf{9x^(2)-4 }`

According to the question,

• 
  `\sf{ (3x − 2)(3x + 2) = ax^(2) − b }`

• 
  `\sf{9x^(2)-4=ax^(2)-b }`

• 
  `\sf{9x^(2)=ax^(2)~and~-4=-b }`

• 
  `\sf{a=9~and~b=4 }`

⠀⠀⠀

`\sf{\bold{\green{\underline{\underline{Answer}}}}}`

Hence,

The value of a is 9

Answer 2

(3x-2)(3x+ 2)

Multiply each term in one set of parentheses by the other terms:

3x x 3x =9x^2

3x x 2 = 6x

-2 x 3x = -6x

-2 x 2 = -4

Combine to get:

9x^2 + 6x - 6x -4

Combine like terms:

9x^2 - 4

The value of a would be 9.